In Mendeleev's original periodic table, the properties of the elements were considered a periodic function of which fundamental quantity?

Introduction / Context:
Before the modern periodic table based on atomic number was developed, Dmitri Mendeleev proposed an earlier form of the periodic table in the 19th century. His arrangement successfully predicted the existence and properties of several undiscovered elements. Understanding what underlying quantity Mendeleev used to arrange elements helps you appreciate the historical development of chemical periodicity and the later shift to the modern atomic number based system.

Given Data / Assumptions:

• The question refers specifically to Mendeleev's periodic table, not the modern long form periodic table.
• Mendeleev worked before the full understanding of atomic number and subatomic particles.
• The options include atomic mass, ionization enthalpy, atomic size, and atomic number.
• We assume the standard historical account taught in school chemistry.

Concept / Approach:
Mendeleev arranged elements in order of increasing atomic mass and observed that their chemical properties repeated periodically. He famously stated that the properties of elements are a periodic function of their atomic masses. Later, modern work by Moseley showed that atomic number, not mass, is the more fundamental quantity, leading to the modern statement that properties are a periodic function of atomic number. For this historical question, however, we need the original Mendeleev formulation, which refers to atomic mass, not atomic number or other properties like ionization enthalpy or atomic size.

Step-by-Step Solution:
Step 1: Identify the period in history. Mendeleev developed his periodic table before the discovery of protons and the modern concept of atomic number. Step 2: Recall the basis of his classification. He arranged elements in order of increasing atomic mass and looked for repeating patterns in properties. Step 3: Recall his periodic law. Mendeleev stated that the properties of elements are a periodic function of their atomic masses. Step 4: Match this statement with the given options.

Verification / Alternative check:
Textbooks on the history of the periodic table clearly distinguish between Mendeleev's Periodic Law and the Modern Periodic Law. Mendeleev's law says properties are a periodic function of atomic mass, while the modern form, based on Moseley's work, states that properties are a periodic function of atomic number. Ionization enthalpy and atomic size are useful trends that can be explained by the periodic table, but they were not used as the primary organising principle by Mendeleev. This historical evidence confirms that Mendeleev's periodic table was mass based.

Why Other Options Are Wrong:
Option B (Ionization enthalpy): Ionization enthalpy is a property we can explain or predict using the periodic table, but it was not the quantity used to arrange elements by Mendeleev. Option C (Atomic size): Atomic radii show periodic trends but were not the basis of Mendeleev's law. Option D (Atomic number): This is the basis of the modern periodic table, but the concept was not known or used in Mendeleev's time.

Common Pitfalls:
A very common mistake is to mix up modern and historical statements and choose atomic number because students remember learning "properties are a periodic function of atomic number". While that is correct for the Modern Periodic Law, the question explicitly mentions Mendeleev's table, which requires the older formulation. Always pay attention to the name or time period mentioned in such questions to avoid this confusion.

Final Answer:
In Mendeleev's periodic table, the properties of the elements were considered a periodic function of their Atomic mass.